// Original: https://github.com/tanakh/competitive-rs #[allow(unused_macros)] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); let mut next = || { iter.next().unwrap() }; input_inner!{next, $($r)*} }; ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } #[allow(unused_macros)] macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => { let mut $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } #[allow(unused_macros)] macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, [ $t:tt ]) => { { let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() } }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, bytes) => { read_value!($next, String).into_bytes() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } #[allow(dead_code)] fn chmin(x: &mut T, y: T) -> bool where T: PartialOrd + Copy, { *x > y && { *x = y; true } } #[allow(dead_code)] fn chmax(x: &mut T, y: T) -> bool where T: PartialOrd + Copy, { *x < y && { *x = y; true } } // Original: koba-e964 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData, } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData, } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { let (mut a, mut b, _) = red(self.x, M::m()); if b < 0 { a = -a; b = -b; } write!(f, "{}/{}", a, b) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } // Finds the simplest fraction x/y congruent to r mod p. // The return value (x, y, z) satisfies x = y * r + z * p. fn red(r: i64, p: i64) -> (i64, i64, i64) { if r.abs() <= 10000 { return (r, 1, 0); } let mut nxt_r = p % r; let mut q = p / r; if 2 * nxt_r >= r { nxt_r -= r; q += 1; } if 2 * nxt_r <= -r { nxt_r += r; q -= 1; } let (x, z, y) = red(nxt_r, r); (x, y - q * z, z) } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } }; } const MOD: i64 = 1_000_000_007; define_mod!(P, MOD); type ModInt = mod_int::ModInt

; /// FFT (in-place, verified as NTT only) /// R: Ring + Copy /// Verified by: https://codeforces.com/contest/1096/submission/47672373 mod fft { use std::ops::*; /// n should be a power of 2. zeta is a primitive n-th root of unity. /// one is unity /// Note that the result should be multiplied by 1/sqrt(n). pub fn transform(f: &mut [R], zeta: R, one: R) where R: Copy + Add + Sub + Mul, { let n = f.len(); assert!(n.is_power_of_two()); { let mut i = 0; for j in 1..n - 1 { let mut k = n >> 1; loop { i ^= k; if k <= i { break; } k >>= 1; } if j < i { f.swap(i, j); } } } let mut zetapow = Vec::new(); { let mut m = 1; let mut cur = zeta; while m < n { zetapow.push(cur); cur = cur * cur; m *= 2; } } let mut m = 1; while m < n { let base = zetapow.pop().unwrap(); let mut r = 0; while r < n { let mut w = one; for s in r..r + m { let u = f[s]; let d = f[s + m] * w; f[s] = u + d; f[s + m] = u - d; w = w * base; } r += 2 * m; } m *= 2; } } } mod arbitrary_mod { use super::fft; use super::mod_int; const MOD1: i64 = 1012924417; const MOD2: i64 = 1224736769; const MOD3: i64 = 1007681537; const G1: i64 = 5; const G2: i64 = 3; const G3: i64 = 3; define_mod!(P1, MOD1); define_mod!(P2, MOD2); define_mod!(P3, MOD3); fn zmod(mut a: i64, b: i64) -> i64 { a %= b; if a < 0 { a += b; } a } fn ext_gcd(mut a: i64, mut b: i64) -> (i64, i64, i64) { let mut x = 0; let mut y = 1; let mut u = 1; let mut v = 0; while a != 0 { let q = b / a; x -= q * u; std::mem::swap(&mut x, &mut u); y -= q * v; std::mem::swap(&mut y, &mut v); b -= q * a; std::mem::swap(&mut b, &mut a); } (b, x, y) } fn invmod(a: i64, b: i64) -> i64 { let x = ext_gcd(a, b).1; zmod(x, b) } // This function is ported from http://math314.hateblo.jp/entry/2015/05/07/014908 fn garner(mut mr: Vec<(i64, i64)>, mo: i64) -> i64 { mr.push((mo, 0)); let mut coffs = vec![1; mr.len()]; let mut constants = vec![0; mr.len()]; for i in 0..mr.len() - 1 { let v = zmod(mr[i].1 - constants[i], mr[i].0) * invmod(coffs[i], mr[i].0) % mr[i].0; assert!(v >= 0); for j in i + 1..mr.len() { constants[j] += coffs[j] * v % mr[j].0; constants[j] %= mr[j].0; coffs[j] = coffs[j] * mr[i].0 % mr[j].0; } } constants[mr.len() - 1] } // f *= g, g is destroyed fn convolution_friendly(a: &[i64], b: &[i64], gen: i64) -> Vec { use mod_int::ModInt; let d = a.len(); let mut f = vec![ModInt::

::new(0); d]; let mut g = vec![ModInt::

::new(0); d]; for i in 0..d { f[i] = a[i].into(); g[i] = b[i].into(); } let zeta = ModInt::new(gen).pow((P::m() - 1) / d as i64); fft::transform(&mut f, zeta, ModInt::new(1)); fft::transform(&mut g, zeta, ModInt::new(1)); for i in 0..d { f[i] *= g[i]; } fft::transform(&mut f, zeta.inv(), ModInt::new(1)); let inv = ModInt::new(d as i64).inv(); let mut ans = vec![0; d]; for i in 0..d { ans[i] = (f[i] * inv).x; } ans } pub fn arbmod_convolution(a: &mut [i64], b: &mut [i64], mo: i64) -> Vec { use super::mod_int::Mod; let d = a.len(); assert!(d.is_power_of_two()); assert_eq!(d, b.len()); for x in a.iter_mut() { *x = zmod(*x, mo); } for x in b.iter_mut() { *x = zmod(*x, mo); } let x = convolution_friendly::(&a, &b, G1); let y = convolution_friendly::(&a, &b, G2); let z = convolution_friendly::(&a, &b, G3); let mut ret = vec![0; d]; let mut mr = [(0, 0); 3]; for i in 0..d { mr[0] = (P1::m(), x[i]); mr[1] = (P2::m(), y[i]); mr[2] = (P3::m(), z[i]); ret[i] = garner(mr.to_vec(), mo); } ret } } // f *= g, g is not destroyed fn convolution(f: &mut [i64], g: &mut [i64]) { let ans = arbitrary_mod::arbmod_convolution(f, g, MOD); for i in 0..f.len() { f[i] = ans[i]; } } fn grow(d: i64, v: i64, mut h: Vec, invfac: &[ModInt]) -> Vec { assert_eq!(h.len() as i64, d + 1); let dd = d as usize; let dm = ModInt::new(d); let vm = ModInt::new(v); let mut aux = vec![1; dd]; let mut f = vec![0; 4 * dd]; let mut g = vec![0; 4 * dd]; for i in 0..dd + 1 { f[i] = (invfac[i] * invfac[dd - i] * h[i]).x; if (dd + i) % 2 != 0 { f[i] = if f[i] == 0 { 0 } else { MOD - f[i] }; } } let oldf = f.clone(); for (idx, &a) in [dm + 1, dm * vm.inv(), dm * vm.inv() + dm + 1] .iter() .enumerate() { for i in 0..4 * dd { f[i] = oldf[i]; } for i in 0..4 * dd { g[i] = 0; } for i in 1..2 * dd + 2 { g[i] = (a - d + i as i64 - 1).inv().x; } convolution(&mut f, &mut g); let mut prod = 1; for i in 0..dd + 1 { prod = prod * (a - i as i64).x % MOD; assert_ne!(prod, 0); } for i in 0..dd + 1 { f[dd + i + 1] = f[dd + i + 1] * prod % MOD; prod = prod * (a + i as i64 + 1).x % MOD; prod = prod * (a - d + i as i64).inv().x % MOD; } match idx { 1 => { for i in 0..dd + 1 { h[i] = h[i] * f[dd + 1 + i] % MOD; } } 0 => { for i in 0..dd { aux[i] = f[dd + 1 + i]; } } 2 => { for i in 0..dd { aux[i] = aux[i] * f[dd + 1 + i] % MOD; } } _ => unreachable!(), } } h.extend_from_slice(&aux); h } fn gen_seq(d: i64, v: i64) -> Vec { assert!(d > 0 && (d as u64).is_power_of_two()); let dd = d as usize; // precompute factorial and its inv let mut fac = vec![ModInt::new(0); 2 * dd + 1]; let mut invfac = vec![ModInt::new(0); 2 * dd + 1]; fac[0] = ModInt::new(1); for i in 1..2 * dd + 1 { fac[i] = fac[i - 1] * (i as i64); } invfac[2 * dd] = fac[2 * dd].inv(); for i in (0..2 * dd).rev() { invfac[i] = invfac[i + 1] * (i as i64 + 1); } let mut size = 1; // Initialized with [g_1(0), g_1(v)]. let mut seq = vec![1.into(), (v + 1).into()]; while size < d { seq = grow(size, v, seq, &invfac); size *= 2; } assert_eq!(size, d); seq } fn fact(n: i64) -> ModInt { let d = 1 << 15; let aux = gen_seq(d, d); // eprintln!("{:?}", aux); let mut ans = ModInt::new(1); let lim = std::cmp::min(d, (n + 1) / d); for i in 0..lim { ans *= aux[i as usize]; } for i in lim * d..n { ans *= i + 1; } ans } fn fact_naive(n: i64) -> ModInt { let mut ans = ModInt::new(1); for i in 1..n + 1 { ans *= i; } ans } #[allow(unused_imports)] use std::cmp::{max, min}; #[allow(unused_imports)] use std::collections::{BTreeMap, BTreeSet, BinaryHeap, VecDeque}; fn main() { input!(n: i64); let a = fact(n); println!("{}", a); }